APPLICATIONS OF ZORN'S LEMMA TO PRIMALS AND GRILLS
SHYAMAPADA MODAK(1), MONOJ KUMAR DAS(2) and CHHAPIKUL MIAH(3)
1. University of Gour Banga, Department of Mathematics , P.O. Mokdumpure, Malda 732 103, INDIA e-mail: spmodak2000@yahoo.co.in 2. University of Gour Banga, Department of Mathematics, P.O. Mokdumpure, Malda 732 103, INDIA e-mail: dmonojkr1@gmail.com 3. Sukanta Mahavidyalaya Department of Mathematics, Dhupguri 735210, West Bengal, INDIA e-mail: chhapikul.77@gmail.com
Abstract
We investigate various connections between the notions of filter, ideal, grill and primal in topological spaces, then we characterize Hausdorff spaces, compact spaces and continuity of functions via limit points and cluster points of grills and primals. As a conclusion on our study on maximal primals, we provide a new proof of Tychonoff theorem.